Question

1. $y = 5sin(pi x)$

Explanation:

Assuming we need to find the amplitude and period of the function \( y = 5\sin(\pi x) \).

Step 1: Recall the general form of a sine function

The general form of a sine function is \( y = A\sin(Bx + C) + D \), where:

• \( |A| \) is the amplitude,
• The period is \( \frac{2\pi}{|B|} \).

Step 2: Identify \( A \) and \( B \) for the given function

For the function \( y = 5\sin(\pi x) \), we have:

• \( A = 5 \)
• \( B = \pi \)

Step 3: Calculate the amplitude

The amplitude is \( |A| \). Since \( A = 5 \), the amplitude is \( |5| = 5 \).

Step 4: Calculate the period

Using the formula for the period \( \frac{2\pi}{|B|} \), substitute \( B = \pi \):
\[
\text{Period} = \frac{2\pi}{|\pi|} = \frac{2\pi}{\pi} = 2
\]

Answer:

• Amplitude: \( 5 \)
• Period: \( 2 \)